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Fast and Efficient Parallel Inversion of Toeplitz and Block Toeplitz Matrices

  • Victor Pan
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 40)

Abstract

We call an n×n matrix A well-conditioned if log(cond A) = O(log n). We compute the inverse of any n×n well-conditioned and diagonally dominant Hermitian Toeplitz matrix A (with errors 1/2N, N = nc for a constant c) by a numerically stable algorithm using O(log2 log log n) parallel arithmetic steps and n log2n/log log n processors. This dramatically improves the previous results. We also compute the inverse and all the coefficients of the characteristic polynomial of any n×n nonsingular Toeplitz matrix A filled with integers (and possibly ill-conditioned) by a distinct algorithm using O(log2n) parallel arithmetic steps, O(n2) processors, and the precision of O(n log(n∥A∥1) binary digits. The results have several modifications, extensions, and further applications.

Keywords

Characteristic Polynomial Toeplitz Matrix Toeplitz Matrice Displacement Generator Pade Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Victor Pan
    • 1
    • 2
  1. 1.Dept. of Math., Lehman CollegeCUNYBronxUSA
  2. 2.Computer Science Dept.SUNY AlbanyAlbanyUSA

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